FOOTNOTES:

[29] _Proc. Arist. Soc._, 1909-1910, pp. 191-218.

[30] On this subject, compare _A Theory of Time and s.p.a.ce_, by Mr.

A.A. Robb (Camb. Univ. Press), which first suggested to me the views advocated here, though I have, for present purposes, omitted what is most interesting and novel in his theory. Mr. Robb has given a sketch of his theory in a pamphlet with the same t.i.tle (Heffer and Sons, Cambridge, 1913).

[31] "Natural Realism and Present Tendencies in Philosophy," _Proc.

Arist. Soc._, 1908-1909, p. 165.

[32] _Die Erfahrungsgrundlagen unseres Wissens_, p. 28.

[33] Cf. _Principia Mathematica_, Vol. I, * 14, and Introduction, Chap. III. For the definition of _existence_, cf. * 14. 02.

[34] Cf. Edwin B. Holt, _The Place of Illusory Experience in a Realistic World._ "The New Realism," p. 303, both on this point and as regards _seeing double_.

IX

ON THE NOTION OF CAUSE

In the following paper I wish, first, to maintain that the word "cause" is so inextricably bound up with misleading a.s.sociations as to make its complete extrusion from the philosophical vocabulary desirable; secondly, to inquire what principle, if any, is employed in science in place of the supposed "law of causality" which philosophers imagine to be employed; thirdly, to exhibit certain confusions, especially in regard to teleology and determinism, which appear to me to be connected with erroneous notions as to causality.

All philosophers, of every school, imagine that causation is one of the fundamental axioms or postulates of science, yet, oddly enough, in advanced sciences such as gravitational astronomy, the word "cause"

never occurs. Dr. James Ward, in his _Naturalism and Agnosticism_, makes this a ground of complaint against physics: the business of those who wish to ascertain the ultimate truth about the world, he apparently thinks, should be the discovery of causes, yet physics never even seeks them. To me it seems that philosophy ought not to a.s.sume such legislative functions, and that the reason why physics has ceased to look for causes is that, in fact, there are no such things.

The law of causality, I believe, like much that pa.s.ses muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm. In order to find out what philosophers commonly understand by "cause," I consulted Baldwin"s _Dictionary_, and was rewarded beyond my expectations, for I found the following three mutually incompatible definitions:--

"CAUSALITY. (1) The necessary connection of events in the time-series....

"CAUSE (notion of). Whatever may be included in the thought or perception of a process as taking place in consequence of another process....

"CAUSE AND EFFECT. (1) Cause and effect ... are correlative terms denoting any two distinguishable things, phases, or aspects of reality, which are so related to each other that whenever the first ceases to exist the second comes into existence immediately after, and whenever the second comes into existence the first has ceased to exist immediately before."

Let us consider these three definitions in turn. The first, obviously, is unintelligible without a definition of "necessary." Under this head, Baldwin"s _Dictionary_ gives the following:--

"NECESSARY. That is necessary which not only is true, but would be true under all circ.u.mstances. Something more than brute compulsion is, therefore, involved in the conception; there is a general law under which the thing takes place."

The notion of cause is so intimately connected with that of necessity that it will be no digression to linger over the above definition, with a view to discovering, if possible, _some_ meaning of which it is capable; for, as it stands, it is very far from having any definite signification.

The first point to notice is that, if any meaning is to be given to the phrase "would be true under all circ.u.mstances," the subject of it must be a propositional function, not a proposition.[35] A proposition is simply true or false, and that ends the matter: there can be no question of "circ.u.mstances." "Charles I"s head was cut off"

is just as true in summer as in winter, on Sundays as on Mondays. Thus when it is worth saying that something "would be true under all circ.u.mstances," the something in question must be a propositional function, i.e. an expression containing a variable, and becoming a proposition when a value is a.s.signed to the variable; the varying "circ.u.mstances" alluded to are then the different values of which the variable is capable. Thus if "necessary" means "what is true under all circ.u.mstances," then "if _x_ is a man, _x_ is mortal" is necessary, because it is true for any possible value of _x_. Thus we should be led to the following definition:--

"NECESSARY is a predicate of a propositional function, meaning that it is true for all possible values of its argument or arguments."

Unfortunately, however, the definition in Baldwin"s _Dictionary_ says that what is necessary is not only "true under all circ.u.mstances" but is also "true." Now these two are incompatible. Only propositions can be "true," and only propositional functions can be "true under all circ.u.mstances." Hence the definition as it stands is nonsense. What is meant seems to be this: "A proposition is necessary when it is a value of a propositional function which is true under all circ.u.mstances, i.e. for all values of its argument or arguments." But if we adopt this definition, the same proposition will be necessary or contingent according as we choose one or other of its terms as the argument to our propositional function. For example, "if Socrates is a man, Socrates is mortal," is necessary if Socrates is chosen as argument, but not if _man_ or _mortal_ is chosen. Again, "if Socrates is a man, Plato is mortal," will be necessary if either Socrates or _man_ is chosen as argument, but not if Plato or _mortal_ is chosen. However, this difficulty can be overcome by specifying the const.i.tuent which is to be regarded as argument, and we thus arrive at the following definition:

"A proposition is _necessary_ with respect to a given const.i.tuent if it remains true when that const.i.tuent is altered in any way compatible with the proposition remaining significant."

We may now apply this definition to the definition of causality quoted above. It is obvious that the argument must be the time at which the earlier event occurs. Thus an instance of causality will be such as: "If the event [Math: e_{1}] occurs at the time [Math: t_{1}], it will be followed by the event [Math: e_{2}]." This proposition is intended to be necessary with respect to [Math: t_{1}], i.e. to remain true however [Math: t_{1}] may be varied. Causality, as a universal law, will then be the following: "Given any event [Math: t_{1}], there is an event [Math: e_{2}] such that, whenever [Math: t_{1}] occurs, [Math: e_{2}] occurs later." But before this can be considered precise, we must specify how much later [Math: e_{2}] is to occur.

Thus the principle becomes:--

"Given any event [Math: e_{1}], there is an event [Math: e_{2}] and a time-interval t such that, whenever [Math: e_{1}] occurs, [Math: e_{2}] follows after an interval t."

I am not concerned as yet to consider whether this law is true or false. For the present, I am merely concerned to discover what the law of causality is supposed to be. I pa.s.s, therefore, to the other definitions quoted above.

The second definition need not detain us long, for two reasons. First, because it is psychological: not the "thought or perception" of a process, but the process itself, must be what concerns us in considering causality. Secondly, because it is circular: in speaking of a process as "taking place in consequence of" another process, it introduces the very notion of cause which was to be defined.

The third definition is by far the most precise; indeed as regards clearness it leaves nothing to be desired. But a great difficulty is caused by the temporal contiguity of cause and effect which the definition a.s.serts. No two instants are contiguous, since the time-series is compact; hence either the cause or the effect or both must, if the definition is correct, endure for a finite time; indeed, by the wording of the definition it is plain that both are a.s.sumed to endure for a finite time. But then we are faced with a dilemma: if the cause is a process involving change within itself, we shall require (if causality is universal) causal relations between its earlier and later parts; moreover, it would seem that only the later parts can be relevant to the effect, since the earlier parts are not contiguous to the effect, and therefore (by the definition) cannot influence the effect. Thus we shall be led to diminish the duration of the cause without limit, and however much we may diminish it, there will still remain an earlier part which might be altered without altering the effect, so that the true cause, as defined, will not have been reached, for it will be observed that the definition excludes plurality of causes. If, on the other hand, the cause is purely static, involving no change within itself, then, in the first place, no such cause is to be found in nature, and in the second place, it seems strange--too strange to be accepted, in spite of bare logical possibility--that the cause, after existing placidly for some time, should suddenly explode into the effect, when it might just as well have done so at any earlier time, or have gone on unchanged without producing its effect. This dilemma, therefore, is fatal to the view that cause and effect can be contiguous in time; if there are causes and effects, they must be separated by a finite time-interval t, as was a.s.sumed in the above interpretation of the first definition.

What is essentially the same statement of the law of causality as the one elicited above from the first of Baldwin"s definitions is given by other philosophers. Thus John Stuart Mill says:--

"The Law of Causation, the recognition of which is the main pillar of inductive science, is but the familiar truth, that invariability of succession is found by observation to obtain between every fact in nature and some other fact which has preceded it."[36]

And Bergson, who has rightly perceived that the law as stated by philosophers is worthless, nevertheless continues to suppose that it is used in science. Thus he says:--

"Now, it is argued, this law [the law of causality] means that every phenomenon is determined by its conditions, or, in other words, that the same causes produce the same effects."[37]

And again:--

"We perceive physical phenomena, and these phenomena obey laws. This means: (1) That phenomena _a_, _b_, _c_, _d_, previously perceived, can occur again in the same shape; (2) that a certain phenomenon P, which appeared after the conditions _a_, _b_, _c_, _d_, and after these conditions only, will not fail to recur as soon as the same conditions are again present."[38]

A great part of Bergson"s attack on science rests on the a.s.sumption that it employs this principle. In fact, it employs no such principle, but philosophers--even Bergson--are too apt to take their views on science from each other, not from science. As to what the principle is, there is a fair consensus among philosophers of different schools.

There are, however, a number of difficulties which at once arise. I omit the question of plurality of causes for the present, since other graver questions have to be considered. Two of these, which are forced on our attention by the above statement of the law, are the following:--

(1) What is meant by an "event"?

(2) How long may the time-interval be between cause and effect?

(1) An "event," in the statement of the law, is obviously intended to be something that is likely to recur since otherwise the law becomes trivial. It follows that an "event" is not a particular, but some universal of which there may be many instances. It follows also that an "event" must be something short of the whole state of the universe, since it is highly improbable that this will recur. What is meant by an "event" is something like striking a match, or dropping a penny into the slot of an automatic machine. If such an event is to recur, it must not be defined too narrowly: we must not state with what degree of force the match is to be struck, nor what is to be the temperature of the penny. For if such considerations were relevant, our "event" would occur at most once, and the law would cease to give information. An "event," then, is a universal defined sufficiently widely to admit of many particular occurrences in time being instances of it.

(2) The next question concerns the time-interval. Philosophers, no doubt, think of cause and effect as contiguous in time, but this, for reasons already given, is impossible. Hence, since there are no infinitesimal time-intervals, there must be some finite lapse of time t between cause and effect. This, however, at once raises insuperable difficulties. However short we make the interval t, something may happen during this interval which prevents the expected result. I put my penny in the slot, but before I can draw out my ticket there is an earthquake which upsets the machine and my calculations. In order to be sure of the expected effect, we must know that there is nothing in the environment to interfere with it. But this means that the supposed cause is not, by itself, adequate to insure the effect. And as soon as we include the environment, the probability of repet.i.tion is diminished, until at last, when the whole environment is included, the probability of repet.i.tion becomes almost _nil_.

In spite of these difficulties, it must, of course, be admitted that many fairly dependable regularities of sequence occur in daily life.

It is these regularities that have suggested the supposed law of causality; where they are found to fail, it is thought that a better formulation could have been found which would have never failed. I am far from denying that there may be such sequences which in fact never do fail. It may be that there will never be an exception to the rule that when a stone of more than a certain ma.s.s, moving with more than a certain velocity, comes in contact with a pane of gla.s.s of less than a certain thickness, the gla.s.s breaks. I also do not deny that the observation of such regularities, even when they are not without exceptions, is useful in the infancy of a science: the observation that unsupported bodies in air usually fall was a stage on the way to the law of gravitation. What I deny is that science a.s.sumes the existence of invariable uniformities of sequence of this kind, or that it aims at discovering them. All such uniformities, as we saw, depend upon a certain vagueness in the definition of the "events." That bodies fall is a vague qualitative statement; science wishes to know how fast they fall. This depends upon the shape of the bodies and the density of the air. It is true that there is more nearly uniformity when they fall in a vacuum; so far as Galileo could observe, the uniformity is then complete. But later it appeared that even there the lat.i.tude made a difference, and the alt.i.tude. Theoretically, the position of the sun and moon must make a difference. In short, every advance in a science takes us farther away from the crude uniformities which are first observed, into greater differentiation of antecedent and consequent, and into a continually wider circle of antecedents recognised as relevant.

The principle "same cause, same effect," which philosophers imagine to be vital to science, is therefore utterly otiose. As soon as the antecedents have been given sufficiently fully to enable the consequent to be calculated with some exact.i.tude, the antecedents have become so complicated that it is very unlikely they will ever recur.

Hence, if this were the principle involved, science would remain utterly sterile.

The importance of these considerations lies partly in the fact that they lead to a more correct account of scientific procedure, partly in the fact that they remove the a.n.a.logy with human volition which makes the conception of cause such a fruitful source of fallacies. The latter point will become clearer by the help of some ill.u.s.trations.

For this purpose I shall consider a few maxims which have played a great part in the history of philosophy.

(1) "Cause and effect must more or less resemble each other." This principle was prominent in the philosophy of occasionalism, and is still by no means extinct. It is still often thought, for example, that mind could not have grown up in a universe which previously contained nothing mental, and one ground for this belief is that matter is too dissimilar from mind to have been able to cause it. Or, more particularly, what are termed the n.o.bler parts of our nature are supposed to be inexplicable, unless the universe always contained something at least equally n.o.ble which could cause them. All such views seem to depend upon a.s.suming some unduly simplified law of causality; for, in any legitimate sense of "cause" and "effect,"

science seems to show that they are usually very widely dissimilar, the "cause" being, in fact, two states of the whole universe, and the "effect" some particular event.

(2) "Cause is a.n.a.logous to volition, since there must be an intelligible _nexus_ between cause and effect." This maxim is, I think, often unconsciously in the imaginations of philosophers who would reject it when explicitly stated. It is probably operative in the view we have just been considering, that mind could not have resulted from a purely material world. I do not profess to know what is meant by "intelligible"; it seems to mean "familiar to imagination." Nothing is less "intelligible," in any other sense, than the connection between an act of will and its fulfilment. But obviously the sort of nexus desired between cause and effect is such as could only hold between the "events" which the supposed law of causality contemplates; the laws which replace causality in such a science as physics leave no room for any two events between which a nexus could be sought.

(3) "The cause _compels_ the effect in some sense in which the effect does not compel the cause." This belief seems largely operative in the dislike of determinism; but, as a matter of fact, it is connected with our second maxim, and falls as soon as that is abandoned. We may define "compulsion" as follows: "Any set of circ.u.mstances is said to compel A when A desires to do something which the circ.u.mstances prevent, or to abstain from something which the circ.u.mstances cause."